Mathematics teacher educators have suggested that preservice mathematics teachers' (PMTs') practices provide evidence of their Mathematical Knowledge for Teaching (MKT). In an effort to explore connections between MKT and PMTs' practices, we developed a framework that operationalizes Ball et al.'s (2008) six MKT domains in terms of approximations…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

Gesture is a powerful and frequent means of mathematical communication. It is a rich modality through which we may reach out to students and they may reach out to teachers, and this is particularly true for instances in which spoken language is not necessarily a commonality among classroom participants. Indeed, our movements help us share more…

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

This report concludes a multiyear series of implementation studies intended to inform the California State University (CSU) system about the implementation of Executive Order 1110 (EO 1110). A major policy established in 2017, EO 1110 requires CSU campuses to eliminate noncredit developmental courses (often known as "remedial" courses)…

Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children's multiple mathematical knowledge bases (MMKB), including children's mathematical thinking and children's home and community-based…

Despite the important role that metacognition plays in school mathematics, attention has only recently turned to primary grades. The aim of this exploratory qualitative study was to find out to what extent 6 second graders engage in metacognitive behaviors during mathematics problem-solving. The analysis was based on the adaptation of the…

Despite the vast research on the early predictors of mathematics achievement, little research has investigated the predictors of various domains of mathematics (e.g., geometry, statistics). The purpose of the present study was to examine the predictive relation between first-grade early numeracy and computation skills and third-grade mathematics…

In this paper, a teaching experience carried out within the framework of the subject of mathematics is presented. This subject is taught at several levels in secondary schools. In addition to some specific content related with mathematics (percentages, fractions, graphics, and bank interest), the methodology is designed in order to enhance the…

Purpose: The students' competencies of math are required to be assessed by using an international scale of evaluation. Thus, education policies and learning evaluation are developed by educational policymakers to improve the education system and result quality. Hence, the purpose of this research was to investigate The Contribution of…

We investigate Open Educational Resources (OER) in post-secondary Calculus with face-to-face instruction using web-based homework in a side-by-side comparison with Closed (Proprietary) Educational Resources (CER). Statistical analyses using multilinear regression models are developed to demonstrate several significant effects, to within a…

This study investigated preservice middle school mathematics teachers' (PSTs) understanding of proportional and nonproportional relationships and their abilities to differentiate these relationships from each other. The PSTs' abilities to interpret and represent proportional and nonproportional situations and solution strategies were also…

This study examined the changes that a group of nine Israeli 7th grade mathematics teachers, who collaborated on editing the textbook they used in class, chose to make in the textbook. Data sources included the project website (using a modified wiki-book platform), the group meetings, interviews with the teachers, individual papers written by the…